Cornell University

Department of Physics

Phys 480/680, Astro 690 April 22, 2005

Computational Physics, Spring 2005

Homework Assignment # 9

(Due Thursday, April 28)

Agenda and readings for the weeks of May 4-7:

Goal: Predict bond length of H$_2$ molecule!

Readings marked NR are from Numerical Recipes: The Art of Scientific Computing, 2$^{\mathrm nd}$ edition (in C). Readings marked LN are from the course lecture notes to be found at http://www.muchomas.lassp.cornell.edu/P480.

Recap of last week of class:

• 04/19 Lec 22: Conjugate gradient algorithm
  Reading: 10.6
• 04/21 Lec 23: FFT
  Reading: 12.2
• 04/21 Lab 8: Finite difference test and numerical precision

Preview of final weeks of class:

• 04/26 Lec 24: Further optimizations for spectral methods; ab initio pseudopotentials

• 04/28 Lec 25: Go directly to lab

• 04/28 Lab 9: Performance of numerical minimization techniques (from Lab 8); quantum states of harmonic oscillator (Lab 7) and quantum dot (Lab 8), physics of hydrogen molecule (Lab 9)

• 05/03 Lec 26: DFT++ expressions for general case of variable fillings
  Reading: Secs. 1-4 of ``New algebraic formulation of density functional calculation,'' by Sohrab Ismail-Beigi and T.A. Arias, Computer Physics Communications 128:1-2, 1-45 (June 2000). Preprint: http://arxiv.org/abs/cond-mat/9909130.

• 05/05 Lec 27: Extraction of eigenstates from variational principle

• 05/05 Lab 10: Electronic structure of crystalline germanium solid

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